\[\boxed{\text{655}\text{\ (655)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x_{1} = 2,\ \ x_{5} = x_{1} \cdot q^{4} = 162,\ \ q < 0;\]
\[162 = 2q^{4},\ \ q^{4} = 81,\ \ q = - 3;\]
\[S_{6} = 2 \cdot \frac{( - 3)^{6} - 1}{- 3 - 1} = - \frac{728}{2} = - 364.\]
\[Ответ: - 364.\]